디랙 방정식

Let there be light.

Start with the relativistic wave equation (Dirac equation).

\(i \gamma^\mu \partial_\mu \psi - m \psi =0\)

Choose a Lagrangian.

\(\mathcal{L} = i \bar{\psi} \gamma^\mu \partial_\mu \psi -m \bar{\psi} \psi\)

We need a \(U(1)\) - local gauge invariance.

\(\psi(x) \to e^{i\alpha(x)}\psi(x)\)

To obtain the local gague invariance, introduce a new gauge field and get

and there was light. God saw that the light was good.

1927, Dirac adopted new equation for relativistic Schrodinger equation to remove negative energy states.
http://www.google.com/search?hl=en&tbs=tl:1&q=
수학사연표

목차